Many watercraft are designed to operate in a planing mode as well as in a displacement mode. In the planing mode of operation, lift is derived from a downward deflection of water by the shape of the hull. In the displacement mode of operation, which generally occurs at lower speeds as compared with planing mode, lift is derived from the weight of water displaced by the hull.
In transition between these modes there is often considerable wave and turbulence drag. This is often due to the conflict in the preferred watercraft design features for displacement mode operation, e.g. a slender/narrow hull, versus preferred features for planing mode operation, e.g. a flat planing bottom or a flat planing bottom with a dead rise angle. A planing bottom may be split in the transverse direction (as in a tunnel boat) or split in the longitudinal direction with displacement in the vertical direction at the split. For most hulls intended to be operable in a planing mode of operation, the bottom shape is generally flat in the longitudinal direction near the back or stern and has rocker toward the bow.
For a wing/deep hydrofoil, as given in the “HYDROFOIL HANDBOOK Vol. II, Hydrodynamics Characteristics of Components”, OTS-US Dept of Commerce, Eq. 1.6, the two-dimensional lift coefficient, CL, is given by:CL=2π(αo+2f/c),  (1)where αo is the attack angle, f is the maximum deviation of the mean camber line from the chord line which goes from the nose to the tail of the wing section, and c is the chord (e.g. front to back dimension; the length of the cord line) of the wing.
Similarly, from this handbook and other sources, for a planing surface, the two-dimensional lift coefficient, CL, at small αo is given by:CL=0.9π(αo+2f/c),  (2)For three dimensional lift coefficient, CL, and a surface which is flat in the width dimension, CL is approximately:CL=0.9π(αo+2f/c)A/(2+A),  (3)where αo is the attack angle, f is the maximum camber of the wetted planing surface, c is the chord of the wetted length of the planing surface at a given speed and load, and “A” is the aspect ratio. Aspect ratio, A, is given by the equation A=b2/area, where b is the width of the planing surface and “area” is the wetted planing area. More accurate values of CL for a flat surface are given by Daniel Savitsky, in “Hydrodynamic Design of Planing Hulls”. Note that hereafter, f is used to mean the maximum camber of the wetted planing surface.
If the wetted planing length includes the above mentioned front rocker, which is a common feature for watercraft expected to transition from displacement mode to planing mode, then “f” is negative and CL is considerably less than that for a flat planing surface having the same wetted length and area. In sailboards and most planing watercraft, this leads to a peak, or larger peak, in the drag when attempting to go from a displacement mode to a planing mode. In power boats it leads to αo increasing to a value much bigger than is optimum and sometimes even produces cavitation of the propeller (i.e. “prop”).
While rocker (negative values of “f”) decreases the planing force (i.e. the lift force on the planing surface), camber (positive values of “f”) can have even worse effects on the performance of a planing surface of a planing hull. Camber at the stern of the hull of a planing power boat, also known as hook and camber, can cause severe porpoising. Even though a cambered surface with αo=0 has no dynamic drag while still having lift, porpoising and the force of the water on the front can cause a watercraft to submerge at the bow.
In general, drag is undesirably increased for a planing hull with a camber at the stern due to the increased wetted area that results from a reduced planing angle. Three examples of this type of camber are given in European patent no. 0059345, and U.S. Pat. Nos. 3,274,966 and 5,582,123.
The effects of net concavity/camber in the longitudinal direction include: 1) at transition speed it will increase the transom depth thus increasing the hump drag and/or 2) will push the bow into the water at high speed. If it does, the drag will be larger. Hump drag is a peak in drag often occurring in the transition mode of a watercraft.
Various hull designs have been developed in an attempt to overcome drawbacks of a mono-hull with a front rocker. Tunnel boats, for example, are efficient in displacement mode and at high planing speed, but due to a reduced planing surface, they require achieving much higher speeds as compared to mono-hulls in order to transition from displacement mode to planing mode.
U.S. Pat. Nos. 3,149,351 and 4,843,988 teach the use of a slot alongside of a planing surface to reduce drag. U.S. Pat. No. 6,138,601 teaches the use of slots above a winglet which are trim tabs at the rear corners.
U.S. Pat. No. 5,456,202 teaches the use of a planing surface in front of a total center of gravity. It is not inclined at a larger attack angle than the other planing surface and is rockered in the front like a normal mono hull power boat. These hulls have the problem that when transitioning to planing mode the step causes turbulence and additional wave drag.
U.S. Pat. No. 3,802,370 teaches a planing surface with a portion having an incline relative to the rest of the planing surface; however, it consists of two longitudinal surfaces which are small and narrow in width compared to the other planing surfaces.
U.S. Pat. No. 6,138,602 describes a hull with a cambered front and a rear planing surface which is rockered in the middle where it would normally be in the water when planing. Thus it would have a downward suction force that will reduce its efficiency at slower planing speeds.
U.S. Pat. No. 4,924,742 teaches using three point planing, a concept which is generally well known in the art. The general concept is to have two sponsons in front of a hull's center of gravity, both sponsons extending below the remaining surfaces of the hull's underside. Various shapes for the sponsons are known. Such three point hydroplanes are designed for planing at over 40 mph. The width of a sponson planing surface is small compared to the width of the hull. This together with the drag behind the sponsons causes the lift/drag to be small when transitioning to the planing mode. Such hulls have the problem that when transitioning to planing the sponsons cause turbulence and additional wave drag, and since the size and lift of the sponsons is small, increased speed is needed for transitioning to planing mode.
Keller in U.S. Pat. No. 7,793,604 and W. Sottorf in NACA TN No. 739, 1934 show that angling or curving the outer edges of a planing surface can increase lift/drag efficiency. Keller shows that a 14° angled/curved outer edge is more efficient than a flat edge. Sottorf shows that surface with a 10 degree dead-rise which curves down at 23° is more efficient than a flat surface for planing angles >6° and has a higher maximum lift/drag vs. planing angle. Sottorf also shows that for a 48° dead rise, a 28.7° edge angle is better than both 0.0° and 48° outer edge angles.
Blount, D. L. and Codega, L. T. in “Dynamic Stability of Planing Boats” Marine Tech. Vol. 29, No. 1, January 1992, pp. 4-12, have shown that hydrodynamic forces on a rocker surface can cause suction, similar to that on the top surface of a wing, and that this can lead to bow down and unstable conditions both in the longitudinal and transverse directions. They and others like Brian Hinde have suggested using steps near this front rockered surface to correct this downward suction force.
Clement, E. P., “A Configuration for a stepped Planing Boat Having Minimum drag (Dynaplane Boat)” and Johnson, V. E. Jr., “Theoretical and Experimental Investigation of Supercavitating Hydrofoils Operating Near the free water Surface” NASA tech. Report R-93 1961. Second edition describe a motorboat design optimized for speeds of 40 to 80 mph and more. The planing surface is small, with a design aspect ratio of 2. At the hump speed, the resistance is shown to be larger than that for a normal motorboat with the same dead rise angle. “Hump speed” is used to refer to the transition speed at which a peak in drag/lift is observed over the range of transition speeds.
Harper, J. A., U.S. Pat. No. 8,122,840 uses a Johnson 3 term camber on the back part of a displacement hull.
For power yachts, size and speed affect the ideal shape. The high speed power boats might be a tunnel boat, a so called cigarette boat, or a three point hydroplane type. For a somewhat lower speed, they may preferably be a type of deep Vee hull. However, particularly in bigger yachts where their size requires a lot of power and a lot of fuel, there is a need for improved efficiency in speeds of 20 mph up to about 35 mph.